Federation of American Scientists

From Wikipedia, the free encyclopedia

Federation of American Scientists
Headquarters	Washington, D.C.
Leaders
• President	Ali Nouri
Establishment
• Founded	6 January 1946
Website fas.org

The Federation of American Scientists (FAS) is a 501(c)(3) organization with the stated intent of using science and scientific analysis to attempt to make the world more secure. FAS was founded in 1945 by scientists who worked on the Manhattan Project to develop the first atomic bombs. The Federation of American Scientists also aims to reduce the amount of nuclear weapons that are in use, and prevent nuclear and radiological terrorism. They hope to present high standards for nuclear energy’s safety and security, illuminate government secrecy practices, as well as track and eliminate the global illicit trade of conventional, nuclear, biological and chemical weapons. With 100 sponsors, the Federation of American Scientists claims that it promotes a safer and more secure world by developing and advancing solutions to important science and technology security policy problems by educating the public and policy makers, and promoting transparency through research and analysis to maximize impact on policy. FAS projects are organized in three main programs: nuclear security, government secrecy, and biosecurity. FAS played a role in the control of atomic energy and weapons, as well as better international monitoring of atomic activities.

History

FAS logo

 

FAS was founded as the Federation of Atomic Scientists on November 30, 1945, by a group of scientists and engineers within the Associations of Manhattan Project Scientists, Oak Ridge Scientists, and Los Alamos Scientists. Its early mission was to support the McMahon Act of 1946, educate the public, press, politicians, and policy-makers, and promote international transparency and nuclear disarmament. The group was frustrated with the control of the nation's nuclear arsenal and advocated for public control of the nuclear arsenal. A group of the early members of the Federation of American Scientists went to Washington D.C. and set up there sending letters to representatives in the House of Representatives and in the Senate to request support for their original goal to not support the May-Johnson Bill. The group of scientists were opposed to the fact that, under the proposed May-Johnson Bill, the United States military would have the majority of control over the development and control of atomic weapons. Working with congressmen, they worked to create the bill that brought forth the Atomic Energy Commission (AEC). The Atomic Energy Commission oversaw the research into atomic energy and atomic weapons. On January 6, 1946, FAS changed its name to the Federation of American Scientists, but its purpose remained the same—to agitate for the international control of atomic energy and its devotion to peaceful uses, public promotion of science and the freedom and integrity of scientists and scientific research. For this purpose, permanent headquarters were set up in Washington, D.C., and contacts were established with the several branches of government, the United Nations, professional and private organizations, and influential persons. The explosion of postwar political activism demonstrated by the group became known as the "scientists' movement" with the basis of being unhappy with the United States' monopoly on nuclear weapons. During this movement, the idea was also established that no defense against an atomic bomb was feasible in the near future. Using these two ideas, the FAS proposed the United States and other technologically advanced nations had to work in unison to create a solution that would not end in complete destruction.

In 1946, the FAS worked with the Ad Council to broadcast a list of facts regarding the state of the United Nations atomic energy negotiations as well as the American proposal for atomic development. In a rare example of an effort to simply give listeners facts with little to no political or personal bias, the scientists at FAS were able to broadcast this information to the public in hopes of informing the public to be "armed with the facts -- instead of swayed by emotions or prejudices." Throughout the course of trying to give the public information, the FAS attempted to coordinate with PR agencies to better connect with the audience. Most of these plans fell through as the agencies typically did not see eye-to-eye with members of the FAS. Scientists realized the importance of getting their point across, but conveying that to someone who had little to no background knowledge on the subject of atomic energy proved to be a challenge, a challenge that would stick with the FAS for many years. Many scientists from more localized organizations had comments like "We have failed. The people have not understood us or our foreign policy would have changed."

By 1948, the Federation had grown to twenty local associations, with 2,500 members, and had been instrumental in the passage of the McMahon Act and the National Science Foundation, and had influenced the American position in the United Nations with regard to international control of atomic energy and disarmament.

In addition to influencing government policy, it undertook a program of public education on the nature and control of atomic energy through lectures, films, exhibits, and the distribution of literature, coordinating its own activities with that of member organizations through the issue of memorandum, policy statements, information sheets, and newsletters. 

Nearly ninety percent of Manhattan Project personnel were in approval of the FAS. With few comparing the group to a "scientists' lobby." 

Mission

The mission of FAS is to promote a safer and more secure world by developing and advancing solutions to important science and technology security policy problems by educating the public and policy makers, and promoting transparency through research and analysis to maximize impact on policy. This mission was established early on and was deemed necessary for the federation, as decisions made by the United States during the conception of the FAS were critical in terms of shaping international relations. The FAS wanted the public to become more critical and aware of the government, in order to monitor the decisions that were made to ensure that they matched what the public actually wanted. The FAS would act to inform the public about how destructive the improper use of atomic energy could be and emphasize the need to enforce international control of atomic weapons and energy.

Membership

In 1969 the FAS had a rough annual budget of $7,000 and relied on mostly volunteer staff. In 1970 Jeremy J. Stone was selected as president of the organization and was the only staff member for the next 5 years. Due to Stone being the president and only member of the organization he influenced the future and direction of the organization heavily. With an increased budget in the 1990s FAS was able to employ a staff of about a dozen people and expand membership of the organization.

In the mid 1980’s the FAS began relying more heavily on journalist, professional staff and analyst rather than famous scientists as it did previously in its history. This showed the organization’s shift towards public information and transparency in the government and away from secrecy in covert projects and finances. In 2000 Henry Kelly became the new president and further perused the goals of the program of bolstering science in policy and focusing on using that science to further benefit the public.

In a 2002 survey conducted within the FAS found that nearly thirty percent of members were physicists. While the next largest fields represented were medicine, biology, engineering, and chemistry. With the latter four fields making up another sixty one percent of the total member population. Members also received complementary copies of "Secrecy News," an electronic newsletter regarding government secrecy and intelligence.

Finances

In the 2004 fiscal year, the FAS ran on a $3 million budget. Over sixty percent of the budget came from private contributions while another third came from government grants. With membership dues alone, the federation achieved a profit of $125,000. The Federation of American Scientists receive many grants for the work that they do. They have received grants from the Ploughshares Fund and from the New Land Foundation for continuing their work to keep the public informed of the state of nuclear weapons across the world. In addition the Federation of American Scientists receives grants from the Carnegie Corporation of New York for their work on the Nuclear Information Project.

Funding from the MacArthur Foundation

Federation of American Scientists was awarded $10,586,000 between 1984 and 2017, including 25 grants in International Peace & Security, MacArthur Award for Creative & Effective Institutions, and Nuclear Challenges. In 2004 the Federation of American Scientists received their largest grant from the MacArthur Foundation of $2,400,000 in support of everything that they do.

The Chronological List of the Grants that the Federation of American Scientists has received from the MacArthur Foundation (As of April 16, 2019) is as follows: 

2018 - The Federation of American Scientists received a grant for $210,000 through the International Peace and Security program. The project title was, "For modifying liability structures and market incentives to give insurance and financial institutions leverage tools to enhance nuclear security." Through this project, the (FAS) will convene a small task force of experts from legal, nuclear, and financial domains to generate and review options for improving nuclear-security-related incentives that apply to insurance companies, banks, and corporations. The task force will seek areas where the law is unsettled or inadequately focused on security risks, and will identify and promote practical steps to address these gaps. This grant is still in use until June 2019. 

2017 - The Federation of American Scientists received two grants, one for $1,870,000 and a second grant for $50,000 to continue their efforts to promote stability in the world. The MacArthur Foundation found that their work with Nuclear Arms and the Nuclear Information Project (see below), and their effort to help with the disposal of nuclear material after using it for nuclear energy was helping the stability and safety of the world.

2015 - The Federation of American Scientists received two grants, one for $684,000 and a second grant for $200,000. The MacArthur foundation awarded them these grants because of the Federation of American Scientist's work in regards to Naval use of nuclear energy, specifically in the nuclear reactors found on aircraft carriers and submarines. In addition to the naval nuclear energy, the MacArthur foundation awarded the second grant of $200,000 so that the Federation of American Scientists could independently verify information about the Iran Nuclear Deal.

2014 - The Federation of American Scientists received a $140,000 grant.

2013 - The Federation of American Scientists received a $145,000 grant for their work on the naval propulsion reactors that work with uranium.

2012 - The Federation of American Scientists received a grant for $50,000 through the International Peace and Security program. This grant was to help assist in strategic planning. It lasted for 12 months. 

2009 - Received a grant for $25,000.

2009- The Federation of American Scientists received a grant for $250,000 through the International Peace and Security program. This grant was in use for 33 months and was used to assist in finding new approaches to nuclear transparency.

2008 - Received a grant for $300,000 to make information about nuclear weapons available to the public.

2007 - The Federation of American Scientists received a grant for $612,318 through the International Peace and Security program. This grant was in use for 48 months, or four years, and was a final grant used toward a project to strengthen the link between the biological research and security policy communities.

2006 - Received a grant for $590,000.

2006 - The Federation of American Scientists received a grant for $500,000 through the International Peace and Security program. This grant was in use for 24 months, and was used toward a project to strengthen the link between the biological research and security policy communities.

2004 - Received a grant for $2,500,000.

Nuclear Security Program

Continuing the FAS tradition of international control of atomic energy and devotion to its peaceful uses, the Nuclear Security Program pursues projects that create a more secure world. The Nuclear Security Program (NSP) includes program work that focuses on reducing the risks of further nuclear proliferation and nuclear terrorism. 

The NSP has key areas of research in order to promote nuclear security around the world. The program focuses on:

• Signatures of nuclear materials and processes 
• Prevention, detection, interdiction, and response for illicit nuclear/radioactive threats
• Applications of nuclear probes for detection of security-relevant materials
• Application of nuclear security in real-world settings
• Policy, law, and diplomacy relating to global nuclear security.

Nuclear Information Project

The Nuclear Information Project provides the general public and policy-makers with information and analysis on the status, number, and operation of nuclear weapons, the policies that guide their potential use and nuclear arms control. The project reports on developments in the nuclear fuel cycle that are relevant to nuclear weapons proliferation. The project puts technical information into a nonproliferation context and looks at case studies by conducting independent calculations and analyses. In addition to covering information over the quantities of nuclear arms in the world, they make it user friendly for those who are not nuclear physicists. In the nuclear fuel part of the report, the Federation of American Scientists covers the state of nuclear fuel and the Global Nuclear Energy Partnership (GNEP). The whole goal of the Nuclear Information Project is to keep the public the most educated on nuclear weapons so that they can make the most educated decisions when it comes to policy making in regards to nuclear energy or nuclear weapons.

The Nuclear Information Project is run by Hans M. Kristensen.

Government Secrecy

The Government Secrecy Project works to promote public access to government information and to illuminate the apparatus of government secrecy, including national security classification and declassification policies. The project also publishes previously undisclosed or hard-to-find government documents of public policy interest, as well as resources on intelligence policy.

The project publication is Secrecy News, which reports on new developments in government secrecy and provides public access to documentary resources on secrecy, intelligence, and national security policy.

The Government Secrecy Project is directed by Steven Aftergood, who is also editor and author of Secrecy News.

Legacy programs and projects

Arms Sales Monitoring Project

The Arms Sales Monitoring Project (ASMP) worked to increase transparency, accountability and restraint in the legal arms trade; eradicate the illicit arms trade; and served as a repository of data on U.S. arms transfers and arms export controls. Project work focused on the arms trade, U.S. arms export policies, and the illicit trade in small arms and light weapons through the publication of reports and articles, media outreach, and public speaking.

The Advisory Board for the Arms Sales Monitoring Project included Ambassador Jayantha Dhanapala, Dr. Bruce Hoffman, and Dr. Moisés Naím. 

The project was sponsored by: CarEth Foundation, Compton Foundation, Inc., Greenville Foundation, John D. and Catherine T. MacArthur Foundation, Stewart R. Mott Charitable Trust,  Ploughshares Fund, Samuel Rubin Foundation, Spanel Foundation, Inc., and Winston Foundation for World Peace.

The Arms Sales Monitoring Project was discontinued in 2014.

Biosecurity Program

The Biosecurity Program concentrates on researching and advocating policies that balance science and security without compromising national security or scientific progress. This includes preventing the misuse of research and promoting the public understanding of the real threats from biological and chemical weapons. The Federation of American Scientists also concentrates on researching and keeping the public informed on genetic engineering and genetic modification as a subset of their biosecurity program. One of their major concerns is resistance that species can develop to certain modifications from genetic resistance or from the use of antibiotics.

The biosecurity program is specifically designed to prevent the use of biological agents and pathogens. Because there have only been few instances in which individuals have attempted to misuse life sciences, the effectiveness of biosecurity programs is currently difficult to detect. Improving biosecurity programs in the future will rely heavily on using metrics to determine outcomes (the impact of what was done). Goals of the programs are quantitative in nature, including an increase in agents secured as well as scientists engaged.

The big concerns with biosecurity are accidental biological threats, intentional malicious biological threats, and natural biological threat occurrences. Because of these threats the Virtual Biosecurity Center (VBC) was set up. 

The Virtual Biosecurity Center (VBC) was founded in 2011 and is spearheaded by the Federation of American Scientists. The VBC is committed to counteracting threats posed by the development of biological weapons as well as ensuring individuals use science and technology responsibly. The Virtual Biosecurity Center provides the public with a resource to find the latest updates on biosecurity policy, bioterrorism information, and biodefense research.

The Virtual Biosecurity Center provides and promotes biosecurity information, education, best practices and collaboration. Additionally, VBC offers significant news and events regarding biosecurity, a regularly updated education center and library, a global forum on Bio risks, an online informative policy tool, empowering partnerships among other professional biosecurity communities around the world, scheduled global conferences to raise awareness and develop plans for current and future biosecurity issues, as well as partnerships to tighten the gap between the scientific, public health, intelligence and law enforcement communities.

In addition to the Virtual Biosecurity Center, the Federation of American Scientists has a public resource available known as the Biosecurity and Biodefence Resource. The purpose of the Biosecurity and Biodefence Resource is to keep the public informed on information about biological policy of governments and research institutes across the world.

Military Analysis Network

The Military Analysis Network offered information on U.S. and Foreign Weapon Systems, Munitions, and Weapons in Space. The Network provided resources and databases in several categories including:

• A guide to United States Munitions and Weapons Systems
• Rest of World Military Equipment by Country Index
• United States Military Logistics Index
• Selected Country Military Summaries Index
• Report on Weapons in Space

This is a legacy project and information is no longer updated by FAS staff.

Learning Technologies Program

The Learning Technologies Program (LTP) focused on ways to use innovative technologies to improve how people teach and learn. The LTP created prototype games and learning tools and assembled collaborative projects consisting of NGOs, design professionals, and community leaders to undertake innovative education initiatives at both the national and local level. 

The Project worked to help create learning tools to bring about major gains in learning and training. The major project of the Program is Immune Attack, a fully 3-D game in which high school students discover the inner workings of the body's circulatory and immune systems, as they pilot a tiny drone through the bloodstream to fight microscopic invaders.

Immune Attack was jointly developed by the Federation of American Scientists, the University of Southern California, Brown University, and Escape Hatch Entertainment. Immune Attack is a supplemental teaching tool, designed to be used in addition to middle school and high school biology textbooks. It introduces molecular biology and cellular biology in detail that is usually reserved for college students. However, it uses the familiar and motivational video game format to introduce the strange and new world of cells and molecules.

The Learning Technologies Program was discontinued in 2013.

Earth Systems Program

The Earth Systems Program (ESP) examined the increased stresses on the environment, including issues relating to energy, food, agriculture, water, and other natural resources, and to analyze how they interact with respect to international security. ESP was created out of the idea that technology should allow people worldwide to improve their living standards and amenities through secure and environmentally friendly ways. The program worked improve dialogue and trust between environmental scientists, policy makers, and the public, as well as to develop science partnerships to solve critical environment and energy problems.

The Earth Systems Program achieves its goals under one specific mission statement:

Over the next century the earth’s resilience and adaptive capabilities will be stressed by the demands of global climate change, environmental degradation, a population of over six billion people, and the accompanying increased resource and energy demand. These stresses will place an additional burden upon the earth’s natural systems and the processes and resources that drive these systems. Future system scarcities and imbalances represent a security concern with the potential to destabilize and weaken existing political, social, and economic structures. And as these natural systems are inherently highly interdependent, it is necessary for them to be analyzed and considered systemically.

To meet their goals, ESP puts a focus on these specific plan areas:

• Transparency
• Technology
• Inquiry
• Policy
• Partnership

Building Technologies Project

The FAS Building Technologies Project was initiated in 2001 to focus the efforts of scientists and engineers who specialize in building materials on a range of issues such as structural engineering, indoor air quality, energy efficiency, and architectural design to create homes that are safe, affordable, and attractive to builders and owners in the United States and abroad. 

The Building Technologies Program worked to advance innovation in building design and construction that can improve quality, affordability, energy efficiency and hazard protection while lowering construction and operating costs. Technical advances, including new composite materials and prefabricated components, help to meet these goals in ways that are beneficial for builders and owners. The Building Technologies Project combined the talents of renowned architects and engineers along with the nation’s leading energy experts to embark upon housing issues in the United States and abroad.

Program areas included:

• Manufactured housing
• Relief housing
• Advanced technologies
• Learning technologies and training
• Policy issues

The Building Technologies Project was discontinued in 2012.

Publications

Some of the recent article and report publications are as follows:

• September 15, 2017, "Nuclear Monitoring and Verification in the Digital Age: Seven Recommendations for Improving the Process"
• August 23, 2017, "The Nonproliferation and Disarmament Challenges of Naval Nuclear Propulsion"
• August 3, 2017, "Nuclear Dynamics in a Multipolar Strategic Ballistic Missile Defense World"
• April 6, 2017, "Life-of-the-Ship Reactors and Accelerated Testing of Naval Propulsion Fuels and Reactors"
• December 5, 2016, "France’s Choice for Naval Nuclear Propulsion: Why Low-Enriched Uranium Was Chosen"
• January 27, 2014: "Negotiated Cuts: A New Nuclear Weapons Treaty Is Not The Only Option"

Leadership

Staff

(as of April 14, 2019)

Steven Aftergood - Director of the Government Secrecy Project, as well as editor of Secrecy News

Hans Kristensen - Director of the Nuclear Information Project

Pia Ulrich - International Nuclear Policy Analyst

Frankie Guarini - Membership, Marketing, and Communications Manager

Ali Nouri - President

Michael Fisher - Senior Fellow

Andrew Choi - Senior Fellow serving in the Office of the President at the World Bank

Adam Mount - Director of Defense Posture Project

The Federation of American Scientists is led by a Board of Directors made up of renowned members of the science, business and academic communities.

Staff Credentials

• Dr. Ali Nouri acquired his B.A. in Biology from Reed College and a Ph. D. in Molecular Biology from Princeton. Prior to becoming president of the Federation of American Scientist he served as a legislative director and national security advisor to a U.S senator Al Franken where he oversaw the senator’s legislative team. Later in 2008 he joined Senator Jim Webb’s and worked as an advisor related to science, energy and the environment. Dr. Nouri was also selected to take part in the New Voices project because of his leadership in science, engineering and medicine.
• Steven Aftergood holds a B.Sc. in electrical engineering from UCLA that he acquired in 1977. He joined the Federation of American Scientist staff in 1989 and from 1992-1998 he was a part of the Aeronautics and Space Engineering Board of the National Research Council. In 1997 Steven Aftergood was the plaintiff in a Freedom of Information Act lawsuit against the CIA which lead to the declassification of the total intelligence budget for the first time and again in 2006 he won another lawsuit against the National Reconnaissance Office for the release of their budget records. Currently he directs the FAS project on Government Secrecy to lessen the national security secrecy and promoting more public access to government information and records.
• Hans M. Kristensen was a Senior Researcher for the Nuclear Information Unit of Greenpeace International in Washington D.C from 1991 to 1996. In 1997-1998 Kristensen served as a Special Advisor to the Danish Ministry of Defense and from 1998 to 2002 he guided the Nuclear Strategy Project at Berkeley, CA. From 2002 to 2005 he was a consultant to the nuclear program for the Natural Resources Defense Council in Washington, D.C where he studied nuclear weapon issues and co-authored on multiple published articles and wrote his own report “U.S. Nuclear Weapons in Europe”. Kristensen was also co-author of the “Nuclear Notebook” column which is referenced as the most accurate source of information on nuclear weapons and facilities.
• Adam Mount has a PhD in government from Georgetown University and has been published by multiple media sources including Foreign Affairs, Survival and Democracy to name a few. He has previously worked as a fellow at the Stanton Nuclear Security on the Council on Foreign Relations and was director of the CFR Independent Task Force on US Policy toward North Korea in 2015-2016.
• Dr. Michael A. Fisher holds a Senior Fellow position for the Federation of American Scientists. Fisher earned a B.S. in Biology at that The College of New Jersey and obtained a Ph. D in Molecular Biology from Princeton University. According to his Linkedin, Fisher joined the FAS in January 2019. Before joining the Federation of American Scientists, Fisher contributed to several different organizations such as: working as a Field Director for the Welle for Congress campaign in New Jersey from March 2018-November 2018, holding title of president and Board Member of the Madison Commons Condominium Association, Inc from February 2015- November 2018, working as a Post Doctoral Fellow at Rutgers University from March 2015- March 2018 and more. Fisher is an expert in infectious disease research, biofuels, synthetic biology, protein engineering, and molecular biology. Fisher has been published in 9 different journals, including an article published in Nature called "Testing the Waters". On his LinkedIn, he has stated his summary as "I believe science and engineering research, STEAM education, and public engagement are essential for advancing our society in a more positive direction, and I am pursuing these threads as a Senior Fellow at the Federation of American Scientists".
• Andrew Choi has a BSE from Princeton University in Operation Research and Financial Engineering. He was a part of an investment team at Insight Venture Partners in New York with a focus on software. Previous to his work at FAS Andrew was the CTO and co-founder of Predata, an AI startup that developed an analytic platform that helps predict geopolitical events and risks. He was also the co-founder of Doceoware, built for open online courses. Currently at the Federation of American Scientists he serves the Office of the President at the World Bank focusing on its Famine Action Mechanism (FAM) to help predict global crises and more economically provide aid and resources to affected areas.
• Pia Ulrich has a degree in International and Comparative Law from the University of Osnabrueck and a masters degree in Security Policy Studies from the George Washington University. Ulrich serves as an International Nuclear Policy Analyst and has since August 2013. Pia Ulrich also served as an Advisory Board Member for the William J. Perry Project on Nuclear Weapons Disarmament from June 2003- September 2013.
• Christopher Bidwell received a BA in Political Science from San Diego State University, a MA in National Security Studies and International Relations from the Naval War College, and a JD in Law from Thomas Jefferson School of Law. Bidwell retired from the U.S. Navy having served as a National Security Counselor and the Middle East Desk Officer at the Defense Threat Reduction Agency (DTRA). Bidwell also serves as an active member of the California Bar and an Interest Group for the American Society of International Law.

Blog Sites

Secrecy News Blog

The Secrecy News Blog (ISSN 1939-1986) is a publication of the Federation of American Scientists project on government secrecy. The secrecy blog provides readers with informal coverage of new developments in secrecy, security and intelligence policies, as well as links to new acquisitions on the FAS website. Typically, the blog is updated with a new publication two to three times a week, or as events arise. In addition to the public blogging page, secrecy news is available if one wishes to subscribe to their emails. Archived issues are available on their website, with articles dating back to September 2000.

Strategic Security Blog

The Strategic Security Blog covers national and international security issues. 

Einstein coefficients

From Wikipedia, the free encyclopedia

Emission lines and absorption lines compared to a continuous spectrum

 

Einstein coefficients are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule. The Einstein A coefficient is related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light.

Spectral lines

In physics, one thinks of a spectral line from two viewpoints.

An emission line is formed when an atom or molecule makes a transition from a particular discrete energy level E₂ of an atom, to a lower energy level E₁, emitting a photon of a particular energy and wavelength. A spectrum of many such photons will show an emission spike at the wavelength associated with these photons.

An absorption line is formed when an atom or molecule makes a transition from a lower, E₁, to a higher discrete energy state, E₂, with a photon being absorbed in the process. These absorbed photons generally come from background continuum radiation (the full spectrum of electromagnetic radiation) and a spectrum will show a drop in the continuum radiation at the wavelength associated with the absorbed photons. 

The two states must be bound states in which the electron is bound to the atom or molecule, so the transition is sometimes referred to as a "bound–bound" transition, as opposed to a transition in which the electron is ejected out of the atom completely ("bound–free" transition) into a continuum state, leaving an ionized atom, and generating continuum radiation.

A photon with an energy equal to the difference E₂ − E₁ between the energy levels is released or absorbed in the process. The frequency ν at which the spectral line occurs is related to the photon energy by Bohr's frequency condition E₂ − E₁ = hν where h denotes Planck's constant.

Emission and absorption coefficients

An atomic spectral line refers to emission and absorption events in a gas in which ${\displaystyle n_{2}}$ is the density of atoms in the upper-energy state for the line, and ${\displaystyle n_{1}}$ is the density of atoms in the lower-energy state for the line. 

The emission of atomic line radiation at frequency ν may be described by an emission coefficient ${\displaystyle \epsilon }$ with units of energy/(time × volume × solid angle). ε dt dV dΩ is then the energy emitted by a volume element ${\displaystyle dV}$ in time ${\displaystyle dt}$ into solid angle ${\displaystyle d\Omega }$. For atomic line radiation,

${\displaystyle \epsilon ={\frac {h\nu }{4\pi }}n_{2}A_{21},}$

where ${\displaystyle A_{21}}$ is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. 

The absorption of atomic line radiation may be described by an absorption coefficient ${\displaystyle \kappa }$ with units of 1/length. The expression κ' dx gives the fraction of intensity absorbed for a light beam at frequency ν while traveling distance dx. The absorption coefficient is given by

${\displaystyle \kappa '={\frac {h\nu }{4\pi }}(n_{1}B_{12}-n_{2}B_{21}),}$

where ${\displaystyle B_{12}}$ and ${\displaystyle B_{21}}$ are the Einstein coefficients for photon absorption and induced emission respectively. Like the coefficient ${\displaystyle A_{21}}$, these are also fixed by the intrinsic properties of the relevant atom for the two relevant energy levels. For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by ${\displaystyle B_{12}}$ and ${\displaystyle B_{21}}$, which may be regarded as positive and negative absorption, which are, respectively, the direct photon absorption, and what is commonly called stimulated or induced emission.

The above equations have ignored the influence of the spectroscopic line shape. To be accurate, the above equations need to be multiplied by the (normalized) spectral line shape, in which case the units will change to include a 1/Hz term. 

For conditions of thermodynamic equilibrium, together the number densities ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$, the Einstein coefficients, and the spectral energy density provide sufficient information to determine the absorption and emission rates.

Equilibrium conditions

The number densities ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$ are set by the physical state of the gas in which the spectral line occurs, including the local spectral radiance (or, in some presentations, the local spectral radiant energy density). When that state is either one of strict thermodynamic equilibrium, or one of so-called "local thermodynamic equilibrium", then the distribution of atomic states of excitation (which includes ${\displaystyle n_{2}}$ and ${\displaystyle n_{1}}$) determines the rates of atomic emissions and absorptions to be such that Kirchhoff's law of equality of radiative absorptivity and emissivity holds. In strict thermodynamic equilibrium, the radiation field is said to be black-body radiation and is described by Planck's law. For local thermodynamic equilibrium, the radiation field does not have to be a black-body field, but the rate of interatomic collisions must vastly exceed the rates of absorption and emission of quanta of light, so that the interatomic collisions entirely dominate the distribution of states of atomic excitation. Circumstances occur in which local thermodynamic equilibrium does not prevail, because the strong radiative effects overwhelm the tendency to the Maxwell–Boltzmann distribution of molecular velocities. For example, in the atmosphere of the Sun, the great strength of the radiation dominates. In the upper atmosphere of the Earth, at altitudes over 100 km, the rarity of intermolecular collisions is decisive. 

In the cases of thermodynamic equilibrium and of local thermodynamic equilibrium, the number densities of the atoms, both excited and unexcited, may be calculated from the Maxwell–Boltzmann distribution, but for other cases, (e.g. lasers) the calculation is more complicated.

Einstein coefficients

In 1916, Albert Einstein proposed that there are three processes occurring in the formation of an atomic spectral line. The three processes are referred to as spontaneous emission, stimulated emission, and absorption. With each is associated an Einstein coefficient, which is a measure of the probability of that particular process occurring. Einstein considered the case of isotropic radiation of frequency ν and spectral energy density ρ(ν).

Various formulations

Hilborn has compared various formulations for derivations for the Einstein coefficients, by various authors. For example, Herzberg works with irradiance and wavenumber. Yariv works with energy per unit volume per unit frequency interval; also; this is how the present account is formulated. Mihalas & Weibel-Mihalas work with radiance and frequency; also Chandrasekhar; also Goody & Yung; Loudon uses angular frequency and radiance.

Spontaneous emission

Schematic diagram of atomic spontaneous emission

 

Spontaneous emission is the process by which an electron "spontaneously" (i.e. without any outside influence) decays from a higher energy level to a lower one. The process is described by the Einstein coefficient A₂₁ (s⁻¹), which gives the probability per unit time that an electron in state 2 with energy ${\displaystyle E_{2}}$ will decay spontaneously to state 1 with energy ${\displaystyle E_{1}}$, emitting a photon with an energy E₂ − E₁ = hν. Due to the energy-time uncertainty principle, the transition actually produces photons within a narrow range of frequencies called the spectral linewidth. If ${\displaystyle n_{i}}$ is the number density of atoms in state i , then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be

${\displaystyle \left({\frac {dn_{2}}{dt}}\right)_{\text{spontaneous}}=-A_{21}n_{2}.}$

The same process results in increasing of the population of the state 1:

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{spontaneous}}=A_{21}n_{2}.}$

Stimulated emission

Schematic diagram of atomic stimulated emission

 

Stimulated emission (also known as induced emission) is the process by which an electron is induced to jump from a higher energy level to a lower one by the presence of electromagnetic radiation at (or near) the frequency of the transition. From the thermodynamic viewpoint, this process must be regarded as negative absorption. The process is described by the Einstein coefficient ${\displaystyle B_{21}}$ (J⁻¹ m³ s⁻²), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 2 with energy ${\displaystyle E_{2}}$ will decay to state 1 with energy ${\displaystyle E_{1}}$, emitting a photon with an energy E₂ − E₁ = hν. The change in the number density of atoms in state 1 per unit time due to induced emission will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{neg. absorb.}}=B_{21}n_{2}\rho (\nu ),}$

where ${\displaystyle \rho (\nu )}$ denotes the spectral energy density of the isotropic radiation field at the frequency of the transition.

Stimulated emission is one of the fundamental processes that led to the development of the laser. Laser radiation is, however, very far from the present case of isotropic radiation.

Photon absorption

Schematic diagram of atomic absorption

 

Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one. The process is described by the Einstein coefficient ${\displaystyle B_{12}}$ (J⁻¹ m³ s⁻²), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 1 with energy ${\displaystyle E_{1}}$ will absorb a photon with an energy E₂ − E₁ = hν and jump to state 2 with energy ${\displaystyle E_{2}}$. The change in the number density of atoms in state 1 per unit time due to absorption will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{pos. absorb.}}=-B_{12}n_{1}\rho (\nu ).}$

Detailed balancing

The Einstein coefficients are fixed probabilities per time associated with each atom, and do not depend on the state of the gas of which the atoms are a part. Therefore, any relationship that we can derive between the coefficients at, say, thermodynamic equilibrium will be valid universally.

At thermodynamic equilibrium, we will have a simple balancing, in which the net change in the number of any excited atoms is zero, being balanced by loss and gain due to all processes. With respect to bound-bound transitions, we will have detailed balancing as well, which states that the net exchange between any two levels will be balanced. This is because the probabilities of transition cannot be affected by the presence or absence of other excited atoms. Detailed balance (valid only at equilibrium) requires that the change in time of the number of atoms in level 1 due to the above three processes be zero:

${\displaystyle 0=A_{21}n_{2}+B_{21}n_{2}\rho (\nu )-B_{12}n_{1}\rho (\nu ).}$

Along with detailed balancing, at temperature T we may use our knowledge of the equilibrium energy distribution of the atoms, as stated in the Maxwell–Boltzmann distribution, and the equilibrium distribution of the photons, as stated in Planck's law of black body radiation to derive universal relationships between the Einstein coefficients.

From Boltzmann distribution we have for the number of excited atomic species i:

${\displaystyle {\frac {n_{i}}{n}}={\frac {g_{i}e^{-E_{i}/kT}}{Z}},}$

where n is the total number density of the atomic species, excited and unexcited, k is Boltzmann's constant, T is the temperature, ${\displaystyle g_{i}}$ is the degeneracy (also called the multiplicity) of state i, and Z is the partition function. From Planck's law of black-body radiation at temperature T we have for the spectral energy density at frequency ν

${\displaystyle \rho _{\nu }(\nu ,T)=F(\nu ){\frac {1}{e^{h\nu /kT}-1}},}$

where

${\displaystyle F(\nu )={\frac {8\pi h\nu ^{3}}{c^{3}}},}$

where ${\displaystyle c}$ is the speed of light and ${\displaystyle h}$ is Planck's constant. 

Substituting these expressions into the equation of detailed balancing and remembering that E₂ − E₁ = hν yields

${\displaystyle A_{21}g_{2}e^{-h\nu /kT}+B_{21}g_{2}e^{-h\nu /kT}{\frac {F(\nu )}{e^{h\nu /kT}-1}}=B_{12}g_{1}{\frac {F(\nu )}{e^{h\nu /kT}-1}},}$

separating to

${\displaystyle A_{21}g_{2}(e^{h\nu /kT}-1)+B_{21}g_{2}F(\nu )=B_{12}g_{1}e^{h\nu /kT}F(\nu ).}$

The above equation must hold at any temperature, so

${\displaystyle B_{21}g_{2}=B_{12}g_{1},}$

and

${\displaystyle -A_{21}g_{2}+B_{21}g_{2}F(\nu )=0.}$

Therefore, the three Einstein coefficients are interrelated by

${\displaystyle {\frac {A_{21}}{B_{21}}}=F(\nu )}$

and

${\displaystyle {\frac {B_{21}}{B_{12}}}={\frac {g_{1}}{g_{2}}}.}$

When this relation is inserted into the original equation, one can also find a relation between ${\displaystyle A_{21}}$ and ${\displaystyle B_{12}}$, involving Planck's law.

Oscillator strengths

The oscillator strength ${\displaystyle f_{12}}$ is defined by the following relation to the cross section ${\displaystyle \sigma }$ for absorption:

${\displaystyle \sigma ={\frac {e^{2}}{4\varepsilon _{0}m_{e}c}}\,f_{12}\,\phi _{\nu }={\frac {\pi e^{2}}{2\varepsilon _{0}m_{e}c}}\,f_{12}\,\phi _{\omega },}$

where ${\displaystyle e}$ is the electron charge, ${\displaystyle m_{e}}$ is the electron mass, and ${\displaystyle \phi _{\nu }}$ and ${\displaystyle \phi _{\omega }}$ are normalized distribution functions in frequency and angular frequency respectively. This allows all three Einstein coefficients to be expressed in terms of the single oscillator strength associated with the particular atomic spectral line:

${\displaystyle B_{12}={\frac {e^{2}}{4\varepsilon _{0}m_{e}h\nu }}f_{12},}$

${\displaystyle B_{21}={\frac {e^{2}}{4\varepsilon _{0}m_{e}h\nu }}{\frac {g_{1}}{g_{2}}}f_{12},}$

${\displaystyle A_{21}={\frac {2\pi \nu ^{2}e^{2}}{\varepsilon _{0}m_{e}c^{3}}}{\frac {g_{1}}{g_{2}}}f_{12}.}$